Bayesian interval mapping of count trait loci based on zero-inflated generalized Poisson regression model

Count phenotypes with excessive zeros are often observed in the biological world. Researchers have studied many statistical methods for mapping the quantitative trait loci (QTLs) of zero-inflated count phenotypes. However, most of the existing methods consist of finding the approximate positions of the QTLs on the chromosome by genome-wide scanning. Additionally, most of the existing methods use the EM algorithm for parameter estimation. In this paper, we propose a Bayesian interval mapping scheme of QTLs for zero-inflated count data. The method takes advantage of a zero-inflated generalized Poisson (ZIGP) regression model to study the influence of QTLs on the zero-inflated count phenotype. The MCMC algorithm is used to estimate the effects and position parameters of QTLs. We use the Haldane map function to realize the conversion between recombination rate and map distance. Monte Carlo simulations are conducted to test the applicability and advantage of the proposed method. The effects of QTLs on the formation of mouse cholesterol gallstones were demonstrated by analyzing an mouse data set.     

Molecular diversity, structure and domestication of grasses

Map-based cloning has been considered problematic for isolating quantitative trait loci (QTLs) due to the confounding phenotypic effects of environment and other QTLs. However, five recent studies, all in plants, have succeeded in cloning QTLs using map-based methods. We review the important features of these studies and evaluate the prospects for broader application of the techniques. Successful map-based cloning requires that QTLs represent single genes that can be isolated in near-isogenic lines, and that genotypes can be unambiguously inferred by progeny testing. In plants or animals for which map-based cloning of genes with discrete phenotypes is feasible, the modified procedures required for QTLs should not be limiting in most cases. The choice between map-based cloning and alternative methods will depend on details of the species and traits being studied.     

Zero-inflated generalized Poisson regression mixture model for mapping quantitative trait loci underlying count trait with many zeros

Phenotypes measured in counts are commonly observed in nature. Statistical methods for mapping quantitative trait loci (QTL) underlying count traits are documented in the literature. The majority of them assume that the count phenotype follows a Poisson distribution with appropriate techniques being applied to handle data dispersion. When a count trait has a genetic basis, “naturally occurring” zero status also reflects the underlying gene effects. Simply ignoring or miss-handling the zero data may lead to wrong QTL inference. In this article, we propose an interval mapping approach for mapping QTL underlying count phenotypes containing many zeros. The effects of QTLs on the zero-inflated count trait are modelled through the zero-inflated generalized Poisson regression mixture model, which can handle the zero inflation and Poisson dispersion in the same distribution. We implement the approach using the EM algorithm with the Newton-Raphson algorithm embedded in the M-step, and provide a genome-wide scan for testing and estimating the QTL effects. The performance of the proposed method is evaluated through extensive simulation studies. Extensions to composite and multiple interval mapping are discussed. The utility of the developed approach is illustrated through a mouse F₂ intercross data set. Significant QTLs are detected to control mouse cholesterol gallstone formation.     

Bayesian robust analysis for genetic architecture of quantitative traits

MOTIVATION: In most quantitative trait locus (QTL) mapping studies, phenotypes are assumed to follow normal distributions. Deviations from this assumption may affect the accuracy of QTL detection and lead to detection of spurious QTLs. To improve the robustness of QTL mapping methods, we replaced the normal distribution for residuals in multiple interacting QTL models with the normal/independent distributions that are a class of symmetric and long-tailed distributions and are able to accommodate residual outliers. Subsequently, we developed a Bayesian robust analysis strategy for dissecting genetic architecture of quantitative traits and for mapping genome-wide interacting QTLs in line crosses. RESULTS: Through computer simulations, we showed that our strategy had a similar power for QTL detection compared with traditional methods assuming normal-distributed traits, but had a substantially increased power for non-normal phenotypes. When this strategy was applied to a group of traits associated with physical/chemical characteristics and quality in rice, more main and epistatic QTLs were detected than traditional Bayesian model analyses under the normal assumption.     

Mapping of Quantitative Trait Loci Underlying Cold Tolerance in Rice Seedlings via High-Throughput Sequencing of Pooled Extremes

Low temperature is a major limiting factor in rice growth and development. Mapping of quantitative trait loci (QTLs) controlling cold tolerance is important for rice breeding. Recent studies have suggested that bulked segregant analysis (BSA) combined with next-generation sequencing (NGS) can be an efficient and cost-effective way for QTL mapping. In this study, we employed NGS-assisted BSA to map QTLs conferring cold tolerance at the seedling stage in rice. By deep sequencing of a pair of large DNA pools acquired from a very large F₃ population (10,800 individuals), we obtained ∼450,000 single nucleotide polymorphisms (SNPs) after strict screening. We employed two statistical methods for QTL analysis based on these SNPs, which yielded consistent results. Six QTLs were mapped on chromosomes 1, 2, 5, 8 and 10. The three most significant QTLs on chromosomes 1, 2 and 8 were validated by comparison with previous studies. Two QTLs on chromosomes 2 and 5 were also identified previously, but at the booting stage rather than the seedling stage, suggesting that some QTLs may function at different developmental stages, which would be useful for cold tolerance breeding in rice. Compared with previously reported QTL mapping studies for cold tolerance in rice based on the traditional approaches, the results of this study demonstrated the advantages of NGS-assisted BSA in both efficiency and statistical power.     

The Human Obesity Gene Map: The 2004 Update

This paper presents the eleventh update of the human obesity gene map, which incorporates published results up to the end of October 2004. Evidence from single‐gene mutation obesity cases, Mendelian disorders exhibiting obesity as a clinical feature, transgenic and knockout murine models relevant to obesity, quantitative trait loci (QTLs) from animal cross‐breeding experiments, association studies with candidate genes, and linkages from genome scans is reviewed. As of October 2004, 173 human obesity cases due to single‐gene mutations in 10 different genes have been reported, and 49 loci related to Mendelian syndromes relevant to human obesity have been mapped to a genomic region, and causal genes or strong candidates have been identified for most of these syndromes. There are 166 genes which, when mutated or expressed as transgenes in the mouse, result in phenotypes that affect body weight and adiposity. The number of QTLs reported from animal models currently reaches 221. The number of human obesity QTLs derived from genome scans continues to grow, and we have now 204 QTLs for obesity‐related phenotypes from 50 genome‐wide scans. A total of 38 genomic regions harbor QTLs replicated among two to four studies. The number of studies reporting associations between DNA sequence variation in specific genes and obesity phenotypes has also increased considerably with 358 findings of positive associations with 113 candidate genes. Among them, 18 genes are supported by at least five positive studies. The obesity gene map shows putative loci on all chromosomes except Y. Overall, >600 genes, markers, and chromosomal regions have been associated or linked with human obesity phenotypes. The electronic version of the map with links to useful publications and genomic and other relevant sites can be found at http:obesitygene.pbrc.edu .     

Sequence polymorphisms cause many false cis eQTLs

Many investigations have reported the successful mapping of quantitative trait loci (QTLs) for gene expression phenotypes (eQTLs). Local eQTLs, where expression phenotypes map to the genes themselves, are of especially great interest, because they are direct candidates for previously mapped physiological QTLs. Here we show that many mapped local eQTLs in genetical genomics experiments do not reflect actual expression differences caused by sequence polymorphisms in cis-acting factors changing mRNA levels. Instead they indicate hybridization differences caused by sequence polymorphisms in the mRNA region that is targeted by the microarray probes. Many such polymorphisms can be detected by a sensitive and novel statistical approach that takes the individual probe signals into account. Applying this approach to recent mouse and human eQTL data, we demonstrate that indeed many local eQTLs are falsely reported as "cis-acting" or "cis" and can be successfully detected and eliminated with this approach.     

The genetic architecture necessary for transgressive segregation is common in both natural and domesticated populations

Segregating hybrids often exhibit phenotypes that are extreme or novel relative to the parental lines. This phenomenon is referred to as transgressive segregation, and it provides a mechanism by which hybridization might contribute to adaptive evolution. Genetic studies indicate that transgressive segregation typically results from recombination between parental taxa that possess quantitative trait loci (QTLs) with antagonistic effects (i.e. QTLs with effects that are in the opposite direction to parental differences for those traits). To assess whether this genetic architecture is common, we tabulated the direction of allelic effects for 3252 QTLs from 749 traits and 96 studies. Most traits (63.6%) had at least one antagonistic QTL, indicating that the genetic substrate for transgressive segregation is common. Plants had significantly more antagonistic QTLs than animals, which agrees with previous reports that transgressive segregation is more common in plants than in animals. Likewise, antagonistic QTLs were more frequent in intra- than in interspecific crosses and in morphological than in physiological traits. These results indicate that transgressive segregation provides a general mechanism for the production of extreme phenotypes at both above and below the species level and testify to the possible creative part of hybridization in adaptive evolution and speciation.     

Association Tests of Multiple Phenotypes: ATeMP

Joint analysis of multiple phenotypes has gained growing attention in genome-wide association studies (GWASs), especially for the analysis of multiple intermediate phenotypes which measure the same underlying complex human disorder. One of the multivariate methods, MultiPhen (O’ Reilly et al. 2012), employs the proportional odds model to regress a genotype on multiple phenotypes, hence ignoring the phenotypic distributions. Despite the flexibilities of MultiPhen, the properties and performance of MultiPhen are not well understood, especially when the phenotypic distributions are non-normal. In fact, it is well known in the statistical literature that the estimation is attenuated when the explanatory variables contain measurement errors. In this study, we first established an equivalence relationship between MultiPhen and the generalized Kendall tau association test, shedding light on why MultiPhen can perform well for joint association analysis of multiple phenotypes. Through the equivalence, we show that MultiPhen may lose power when the phenotypes are non-normal. To maintain the power, we propose two solutions (ATeMP-rn and ATeMP-or) to improve MultiPhen, and demonstrate their effectiveness through extensive simulation studies and a real case study from the Guangzhou Twin Eye Study.     

The human obesity gene map: the 2005 update

This paper presents the 12th update of the human obesity gene map, which incorporates published results up to the end of October 2005. Evidence from single-gene mutation obesity cases, Mendelian disorders exhibiting obesity as a clinical feature, transgenic and knockout murine models relevant to obesity, quantitative trait loci (QTL) from animal cross-breeding experiments, association studies with candidate genes, and linkages from genome scans is reviewed. As of October 2005, 176 human obesity cases due to single-gene mutations in 11 different genes have been reported, 50 loci related to Mendelian syndromes relevant to human obesity have been mapped to a genomic region, and causal genes or strong candidates have been identified for most of these syndromes. There are 244 genes that, when mutated or expressed as transgenes in the mouse, result in phenotypes that affect body weight and adiposity. The number of QTLs reported from animal models currently reaches 408. The number of human obesity QTLs derived from genome scans continues to grow, and we now have 253 QTLs for obesity-related phenotypes from 61 genome-wide scans. A total of 52 genomic regions harbor QTLs supported by two or more studies. The number of studies reporting associations between DNA sequence variation in specific genes and obesity phenotypes has also increased considerably, with 426 findings of positive associations with 127 candidate genes. A promising observation is that 22 genes are each supported by at least five positive studies. The obesity gene map shows putative loci on all chromosomes except Y. The electronic version of the map with links to useful publications and relevant sites can be found at http://obesitygene.pbrc.edu.     

Multi-locus test conditional on confirmed effects leads to increased power in genome-wide association studies

Complex diseases or phenotypes may involve multiple genetic variants and interactions between genetic, environmental and other factors. Current genome-wide association studies (GWAS) mostly used single-locus analysis and had identified genetic effects with multiple confirmations. Such confirmed single-nucleotide polymorphism (SNP) effects were likely to be true genetic effects and ignoring this information in testing new effects of the same phenotype results in decreased statistical power due to increased residual variance that has a component of the omitted effects. In this study, a multi-locus association test (MLT) was proposed for GWAS analysis conditional on SNPs with confirmed effects to improve statistical power. Analytical formulae for statistical power were derived and were verified by simulation for MLT accounting for confirmed SNPs and for single-locus test (SLT) without accounting for confirmed SNPs. Statistical power of the two methods was compared by case studies with simulated and the Framingham Heart Study (FHS) GWAS data. Results showed that the MLT method had increased statistical power over SLT. In the GWAS case study on four cholesterol phenotypes and serum metabolites, the MLT method improved statistical power by 5% to 38% depending on the number and effect sizes of the conditional SNPs. For the analysis of HDL cholesterol (HDL-C) and total cholesterol (TC) of the FHS data, the MLT method conditional on confirmed SNPs from GWAS catalog and NCBI had considerably more significant results than SLT.     

Complete genome searches for quantitative trait loci controlling blood pressure and related traits in four segregating populations derived from Dahl hypertensive rats

The Dahl salt-sensitive rat is one of the principal animal models of hereditary hypertension. Genome-wide searches were undertaken to detect quantitative trait loci (QTLs) that influence blood pressure, cardiac mass, and body weight in four F₂ populations derived from Dahl salt-sensitive rats and different inbred normotensive control strains of rat. We detected three QTLs associated with one or more of the phenotypes, using a stringent statistical criterion for linkage (p < 0.00003). These included a novel QTL linked to blood pressure on rat Chromosome (Chr) 12, and another QTL on rat Chr 3 linked to body weight. A QTL on rat Chr 10 for which linkage to blood pressure has been described in other crosses was found to be a principal determinant of blood pressure and cardiac mass in some but not all of the crosses examined here. Three other regions showed evidence of linkage to these phenotypes with a less stringent statistical criterion of linkage at QTLs previously reported in other studies. As part of our study, microsatellite markers have been developed for three candidate genes for investigation in hypertension, and the genes have been localized by linkage mapping. These are: the rat Gs alpha subunit (Gnas) gene, the alpha-1B adrenergic receptor (Adra1b), and the Na⁺, K⁺-ATPase beta2 subunit (Atp1b2) gene. Received: 29 June 1998 / Accepted: 30 October 1998     

The statistics of bulk segregant analysis using next generation sequencing

We describe a statistical framework for QTL mapping using bulk segregant analysis (BSA) based on high throughput, short-read sequencing. Our proposed approach is based on a smoothed version of the standard G statistic, and takes into account variation in allele frequency estimates due to sampling of segregants to form bulks as well as variation introduced during the sequencing of bulks. Using simulation, we explore the impact of key experimental variables such as bulk size and sequencing coverage on the ability to detect QTLs. Counterintuitively, we find that relatively large bulks maximize the power to detect QTLs even though this implies weaker selection and less extreme allele frequency differences. Our simulation studies suggest that with large bulks and sufficient sequencing depth, the methods we propose can be used to detect even weak effect QTLs and we demonstrate the utility of this framework by application to a BSA experiment in the budding yeast Saccharomyces cerevisiae.     

Quantitative trait loci for sensitivity to ethanol intoxication in a C57BL/6J?×?129S1/SvImJ inbred mouse cross

Individual variation in sensitivity to acute ethanol (EtOH) challenge is associated with alcohol drinking and is a predictor of alcohol abuse. Previous studies have shown that the C57BL/6J (B6) and 129S1/SvImJ (S1) inbred mouse strains differ in responses on certain measures of acute EtOH intoxication. To gain insight into genetic factors contributing to these differences, we performed quantitative trait locus (QTL) analysis of measures of EtOH-induced ataxia (accelerating rotarod), hypothermia, and loss of righting reflex (LORR) duration in a B6×S1 F2 population. We confirmed that S1 showed greater EtOH-induced hypothermia (specifically at a high dose) and longer LORR compared to B6. QTL analysis revealed several additive and interacting loci for various phenotypes, as well as examples of genotype interactions with sex. QTLs for different EtOH phenotypes were largely non-overlapping, suggesting separable genetic influences on these behaviors. The most compelling main-effect QTLs were for hypothermia on chromosome 16 and for LORR on chromosomes 4 and 6. Several QTLs overlapped with loci repeatedly linked to EtOH drinking in previous mouse studies. The architecture of the traits we examined was complex but clearly amenable to dissection in future studies. Using integrative genomics strategies, plausible functional and positional candidates may be found. Uncovering candidate genes associated with variation in these phenotypes in this population could ultimately shed light on genetic factors underlying sensitivity to EtOH intoxication and risk for alcoholism in humans.     

Nonparametric functional mapping of quantitative trait loci underlying programmed cell death

The development of an organism represents a complex dynamic process, which is controlled by a network of genes and multiple environmental factors. Programmed cell death (PCD), a physiological cell suicide process, occurs during the development of most organisms and is, typically, a complex dynamic trait. Understanding how genes control this complex developmental process has been a long-standing topic in PCD studies. In this article, we propose a nonparametric model, based on orthogonal Legendre polynomials, to map genes or quantitative trait loci (QTLs) that govern the dynamic features of the PCD process. The model is built under the maximum likelihood-based functional mapping framework and is implemented with the EM algorithm. A general information criterion is proposed for selecting the optimal Legendre order that best fits the dynamic pattern of the PCD process. The consistency of the order selection criterion is established. A nonstationary structured antedependence model (SAD) is applied to model the covariance structure among the phenotypes measured at different time points. The developed model generates a number of hypothesis tests regarding the genetic control mechanism of the PCD process. Extensive simulation studies are conducted to investigate the statistical behavior of the model. Finally, we apply the model to a rice tiller number data set in which several QTLs are identified. The developed model provides a quantitative and testable framework for assessing the interplay between genes and the developmental PCD process, and will have great implications for elucidating the genetic architecture of the PCD process.     

Enhanced statistical tests for GWAS in admixed populations: assessment using African Americans from CARe and a Breast Cancer Consortium

While genome-wide association studies (GWAS) have primarily examined populations of European ancestry, more recent studies often involve additional populations, including admixed populations such as African Americans and Latinos. In admixed populations, linkage disequilibrium (LD) exists both at a fine scale in ancestral populations and at a coarse scale (admixture-LD) due to chromosomal segments of distinct ancestry. Disease association statistics in admixed populations have previously considered SNP association (LD mapping) or admixture association (mapping by admixture-LD), but not both. Here, we introduce a new statistical framework for combining SNP and admixture association in case-control studies, as well as methods for local ancestry-aware imputation. We illustrate the gain in statistical power achieved by these methods by analyzing data of 6,209 unrelated African Americans from the CARe project genotyped on the Affymetrix 6.0 chip, in conjunction with both simulated and real phenotypes, as well as by analyzing the FGFR2 locus using breast cancer GWAS data from 5,761 African-American women. We show that, at typed SNPs, our method yields an 8% increase in statistical power for finding disease risk loci compared to the power achieved by standard methods in case-control studies. At imputed SNPs, we observe an 11% increase in statistical power for mapping disease loci when our local ancestry-aware imputation framework and the new scoring statistic are jointly employed. Finally, we show that our method increases statistical power in regions harboring the causal SNP in the case when the causal SNP is untyped and cannot be imputed. Our methods and our publicly available software are broadly applicable to GWAS in admixed populations.     

Segregation analysis of phenotypic components of learning disabilities. I. Nonword memory and digit span

Dyslexia is a common and complex disorder with evidence for a genetic component. Multiple loci (i.e., quantitative-trait loci [QTLs]) are likely to be involved, but the number is unknown. Diagnosis is complicated by the lack of a standard protocol, and many diagnostic measures have been proposed as understanding of the component processes has evolved. One or more genes may, in turn, influence these measures. To date, little work has been done to evaluate the mode of inheritance of individual component-as opposed to composite-phenotypes, beyond family or twin correlation studies that initially demonstrate evidence for a genetic basis of such components. Here we use two approaches to segregation analysis in 102 nuclear families to estimate genetic models for component phenotypes associated with dyslexia: digit span and a nonword-repetition task. Both measures are related to phonological skills, one of the key component processes in dyslexia. We use oligogenic-trait segregation analysis to estimate the number of QTLs contributing to each phenotype, and we use complex segregation analysis to identify the most parsimonious inheritance models. We provide evidence in support of both a major-gene mode of inheritance for the nonword-repetition task, with approximately 2.4 contributing QTLs, and for a genetic basis of digit span, with approximately 1.9 contributing QTLs. Results obtained by reciprocal adjustment of measures suggest that genes contributing to digit span may contribute to the nonword-repetition score but that there are additional QTLs involved in nonword repetition. Our study adds to existing studies of the genetic basis of composite phenotypes related to dyslexia, by providing evidence for major-gene modes of inheritance of these single-measure component phenotypes.     

Mapping the genetic architecture of complex traits in experimental populations

SUMMARY: Understanding how interactions among set of genes affect diverse phenotypes is having a greater impact on biomedical research, agriculture and evolutionary biology. Mapping and characterizing the isolated effects of single quantitative trait locus (QTL) is a first step, but we also need to assemble networks of QTLs and define non-additive interactions (epistasis) together with a host of potential environmental modulators. In this article, we present a full-QTL model with which to explore the genetic architecture of complex trait in multiple environments. Our model includes the effects of multiple QTLs, epistasis, QTL-by-environment interactions and epistasis-by-environment interactions. A new mapping strategy, including marker interval selection, detection of marker interval interactions and genome scans, is used to evaluate putative locations of multiple QTLs and their interactions. All the mapping procedures are performed in the framework of mixed linear model that are flexible to model environmental factors regardless of fix or random effects being assumed. An F-statistic based on Henderson method III is used for hypothesis tests. This method is less computationally greedy than corresponding likelihood ratio test. In each of the mapping procedures, permutation testing is exploited to control for genome-wide false positive rate, and model selection is used to reduce ghost peaks in F-statistic profile. Parameters of the full-QTL model are estimated using a Bayesian method via Gibbs sampling. Monte Carlo simulations help define the reliability and efficiency of the method. Two real-world phenotypes (BXD mouse olfactory bulb weight data and rice yield data) are used as exemplars to demonstrate our methods. AVAILABILITY: A software package is freely available at http://ibi.zju.edu.cn/software/qtlnetwork     

Human QTL linkage mapping

Human quantitative trait locus (QTL) linkage mapping, although based on classical statistical genetic methods that have been around for many years, has been employed for genome-wide screening for only the last 10–15 years. In this time, there have been many success stories, ranging from QTLs that have been replicated in independent studies to those for which one or more genes underlying the linkage peak have been identified to a few with specific functional variants that have been confirmed in in vitro laboratory assays. Despite these successes, there is a general perception that linkage approaches do not work for complex traits, possibly because many human QTL linkage studies have been limited in sample size and have not employed the family configurations that maximize the power to detect linkage. We predict that human QTL linkage studies will continue to be productive for the next several years, particularly in combination with RNA expression level traits that are showing evidence of regulatory QTLs of large effect sizes and in combination with high-density genome-wide SNP panels. These SNP panels are being used to identify QTLs previously localized by linkage and linkage results are being used to place informative priors on genome-wide association studies.     

Complex genetics controls natural variation among seed quality phenotypes in a recombinant inbred population of an interspecific cross between Solanum lycopersicum × Solanum pimpinellifolium

Seed quality in tomato is associated with many complex physiological and genetic traits. While plant processes are frequently controlled by the action of small‐ to large‐effect genes that follow classic Mendelian inheritance, our study suggests that seed quality is primarily quantitative and genetically complex. Using a recombinant inbred line population of Solanum lycopersicum × Solanum pimpinellifolium, we identified quantitative trait loci (QTLs) influencing seed quality phenotypes under non‐stress, as well as salt, osmotic, cold, high‐temperature and oxidative stress conditions. In total, 42 seed quality traits were analysed and 120 QTLs were identified for germination traits under different conditions. Significant phenotypic correlations were observed between germination traits under optimal conditions, as well as under different stress conditions. In conclusion, one or more QTLs were identified for each trait with some of these QTLs co‐locating. Co‐location of QTLs for different traits can be an indication that a locus has pleiotropic effects on multiple traits due to a common mechanistic basis. However, several QTLs also dissected seed quality in its separate components, suggesting different physiological mechanisms and signalling pathways for different seed quality attributes.